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<h1 class="ltx_title ltx_title_section">Averaging (Box) filter</h1>

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<p class="ltx_p">Applying an averaging filter (also known as mean or box filter) results
in an image in which the value of each pixel is equal to the average
intensity of pixels from the input image in a given neighborhood.
Filtering can be defined as a <a href="Convolution.html" title="" class="ltx_ref">convolution</a>
of the image with a kernel given by an <img id="Sx1.p1.m1" class="ltx_Math" style="vertical-align:-3px" src="mi/mi7.png" width="37" height="18" alt="l\times l"> matrix containing
equal entries that sum to one, thus</p>
<table id="Sx1.Ex1" class="ltx_equation">

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<td class="ltx_align_center"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-35px" src="mi/mi1.png" width="208" height="79" alt="K_{\mathrm{AV}}=\frac{1}{l^{2}}\left[\begin{array}[]{ccc}1&amp;\cdots&amp;1\\
\vdots&amp;\ddots&amp;\vdots\\
1&amp;\cdots&amp;1\end{array}\right]\,."></td>
<td class="ltx_eqn_pad"></td>
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<div id="Sx1.p2" class="ltx_para">
<p class="ltx_p">Kernel <img id="Sx1.p2.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi2.png" width="39" height="18" alt="K_{\mathrm{AV}}"> is separable and the vector <img id="Sx1.p2.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi3.png" width="15" height="16" alt="\boldsymbol{k}">
(see <a href="Convolution.html" title="" class="ltx_ref">convolution with separable kernels</a>)
can be composed from values <img id="Sx1.p2.m3" class="ltx_Math" style="vertical-align:-6px" src="mi/mi5.png" width="66" height="21" alt="k_{i}=1/l">, where <img id="Sx1.p2.m4" class="ltx_Math" style="vertical-align:-5px" src="mi/mi4.png" width="87" height="19" alt="i=1,\ldots,l">. The
kernel size <img id="Sx1.p2.m5" class="ltx_Math" style="vertical-align:-2px" src="mi/mi6.png" width="10" height="16" alt="l"> is a user-specified parameter.</p>
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<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">Threshold for approximate localization of molecules</h2>

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<p class="ltx_p">The <a href="../../detectors/Threshold.html" title="" class="ltx_ref">threshold</a> value can be
specified by users as an expression combining mathematical functions
and operators with variables based on the current raw or filtered
image. Variables provided by this filter are:
</p>
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<td class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">Box.I</span></td>
<td class="ltx_td ltx_align_left">current raw input image</td>
</tr>
<tr class="ltx_tr">
<td class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">Box.F</span></td>
<td class="ltx_td ltx_align_left">corresponding filtered image</td>
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<div id="Sx1.SSx2" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

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<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="Filters.html" title="" class="ltx_ref">Image filtering and feature enhancement</a></p>
</div>
</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="../../detectors/Detectors.html" title="" class="ltx_ref">Finding approximate positions of molecules</a></p>
</div>
</li>
</ul>
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